A unified analysis of stochastic adaptive control: asymptotic self-tuning

The second part of a unified approach to analyzing parametric stochastic adaptive control is presented. In the first stage, the potential self-tuning issue was introduced and examined, where the authors studied self-tuning of stochastic adaptive control schemes at the possible limit points of the parameter estimates, independent of the algorithm used for estimation. In this paper, by considering a general class of estimation algorithms, the authors attempt to determine the conditions under which a certainty-equivalence (CE) based stochastic adaptive control scheme is asymptotically self-tuning. A set of general properties satisfied by some common estimation algorithms, such as stochastic gradient (SG) and weighted extended least squares (WELS), are considered. Based on these assumptions, it is shown that certain sufficient conditions for respectively, potential self-tuning or potential identifiability are also sufficient for asymptotic self-tuning or strong consistency.

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